5-28-2009
MK Big Idea: Many real world situations can be modeled and predicted using mathematics. Essential Question #3: How can technology help us explore linear patterns in the world? 3.2 Graphing Lines
i. y=3x ii. y=-2x iii. y=5x-3 iv. y=-x+6 v. y=2 A.Q: What does each pledge plan mean? A: (i) This means you pay 3$s per mile.
(ii) This means they give you 2$s per mile.
(iii) This means you pay 5$s per mile, then, they give you 3$s back.
(iv) This means they give you 1$s per mile, then you have to pay 6$s.
(v) This means it doesn't matter how many miles you run, you only give 2$s. B.Q: Without your graphing calculator, make a table with the x-values of 1, 2, 3, 4, and 5. Use these table to decide which plan is reasonable. Explain why. A:
Table of different plans
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
of miles ran
y=3x
y=-2x
y=5x-3
y=-x+6
y=2
1
3$
-2$
2$
5$
2$
2
6$
-4$
7$
4$
2$
3
9$
-6$
12$
3$
2$
4
12$
-8$
17$
2$
2$
5
15$
-10$
22$
1$
2$
I think plan 3 is the best one because it makes the most money. Also, even if it isn't, it sounds like a good deal since they give you back 3$s. C.Q: Graph each plan in a graphing calculator. Use a window that shows the graph clearly. Make a sketch of the graph you see. A: D. Q: For each pledge plan, tell whether the y-value increase. decrease, or stay the same as the x-value increase. How can you tell from the graph? From the table? From the equation? A: Plan i: The y-value increases as the x-value does. In the table, both values increase. In the graph, it's shown as a line that goes from the 3rd quadrant up to the 1st quadrant. In the equation, it has a positive coeficient.
Plan ii: The y-value decreases as the x-value icreases. In the table, the x-value increases while the y-value decreases. In the graph, it's shown as a line that goes from the 4th quadrant up to the 2nd quadrant. In the equation, it has a negative coeficient.
Plan iii: The y-value increases as the x-value does. In the table, both values increase. In the graph, it's shown as a line that goes from the 3rd quadrant up to the 1st quadrant while passing the 4th quadrant because it has an negative y-intercept. In the equation, it has a positive coeficient with a additional '-3'.
Plan iv: The y-value decreases as the x-value icreases. In the table, the x-value increases while the y-value decreases. In the graph, it's shown as a line that goes from the 4th quadrant up to the 2nd quadrant while passing the 1st quadrant because of the positive y-intercept. In the equation, it has a negative coeficient with a additional '+6'.
Plan v: The y-value just stays same all the way while the x-value increases. In the table, it shows the same y-value as you go down. In the graph, there is a horizontal line parralel to the x-value that keeps on going forever. In the equation, there's only the y-variable with no x-variable and only the '2'. 3,2 Follow-Up
1. Q: For each of the five pledge plans, give the coordinates of the points where the line crosses the x and the y-axes. (Check that the coordinates you gave fit the equation. Sometimes the decimal values your calculator gives are only approximations.) A: Plan i: x= (0,0) y= (0,0)
Plan ii: x= (0,0) y= (0,0)
Plan iii: x= (3/5,0) y= (0,-3)
Plan iv: x= (6,0) y= (0,6)
Plan v: x= (uhhh... this doesn't have one) y= (0,2) 2. Q: Ali says that x=-1 makes the equation -8=-3+5x true. Tamara tries this value in the equation. She says Ali is wrong because -3+5(-1) is -2, not -8. Why do you think these students found different answers. A: I think its because they had different problem solving orders.
Ali: -3+5(-1)= -3+(5*-1)= -3+-5= -8
Tamara: -3+5(-1)= (-3+5)*-1= 2*-1= -2
MK
Big Idea: Many real world situations can be modeled and predicted using mathematics.
Essential Question #3: How can technology help us explore linear patterns in the world?
3.2 Graphing Lines
i. y=3x ii. y=-2x iii. y=5x-3 iv. y=-x+6 v. y=2
A. Q: What does each pledge plan mean?
A: (i) This means you pay 3$s per mile.
(ii) This means they give you 2$s per mile.
(iii) This means you pay 5$s per mile, then, they give you 3$s back.
(iv) This means they give you 1$s per mile, then you have to pay 6$s.
(v) This means it doesn't matter how many miles you run, you only give 2$s.
B. Q: Without your graphing calculator, make a table with the x-values of 1, 2, 3, 4, and 5. Use these table to decide which plan is reasonable. Explain why.
A:
C. Q: Graph each plan in a graphing calculator. Use a window that shows the graph clearly. Make a sketch of the graph you see.
A:
D. Q: For each pledge plan, tell whether the y-value increase. decrease, or stay the same as the x-value increase. How can you tell from the graph? From the table? From the equation?
A: Plan i: The y-value increases as the x-value does. In the table, both values increase. In the graph, it's shown as a line that goes from the 3rd quadrant up to the 1st quadrant. In the equation, it has a positive coeficient.
Plan ii: The y-value decreases as the x-value icreases. In the table, the x-value increases while the y-value decreases. In the graph, it's shown as a line that goes from the 4th quadrant up to the 2nd quadrant. In the equation, it has a negative coeficient.
Plan iii: The y-value increases as the x-value does. In the table, both values increase. In the graph, it's shown as a line that goes from the 3rd quadrant up to the 1st quadrant while passing the 4th quadrant because it has an negative y-intercept. In the equation, it has a positive coeficient with a additional '-3'.
Plan iv: The y-value decreases as the x-value icreases. In the table, the x-value increases while the y-value decreases. In the graph, it's shown as a line that goes from the 4th quadrant up to the 2nd quadrant while passing the 1st quadrant because of the positive y-intercept. In the equation, it has a negative coeficient with a additional '+6'.
Plan v: The y-value just stays same all the way while the x-value increases. In the table, it shows the same y-value as you go down. In the graph, there is a horizontal line parralel to the x-value that keeps on going forever. In the equation, there's only the y-variable with no x-variable and only the '2'.
3,2 Follow-Up
1. Q: For each of the five pledge plans, give the coordinates of the points where the line crosses the x and the y-axes. (Check that the coordinates you gave fit the equation. Sometimes the decimal values your calculator gives are only approximations.)
A: Plan i: x= (0,0) y= (0,0)
Plan ii: x= (0,0) y= (0,0)
Plan iii: x= (3/5,0) y= (0,-3)
Plan iv: x= (6,0) y= (0,6)
Plan v: x= (uhhh... this doesn't have one) y= (0,2)
2. Q: Ali says that x=-1 makes the equation -8=-3+5x true. Tamara tries this value in the equation. She says Ali is wrong because -3+5(-1) is -2, not -8. Why do you think these students found different answers.
A: I think its because they had different problem solving orders.
Ali: -3+5(-1)= -3+(5*-1)= -3+-5= -8
Tamara: -3+5(-1)= (-3+5)*-1= 2*-1= -2